Magnetic field driven instability in planar NJL model in real-time formalism

O. V. Gamayun; E. V. Gorbar; V. P. Gusynin

doi:10.1103/PhysRevD.86.065021

paper

Magnetic field driven instability in planar NJL model in real-time formalism

arXiv:1206.2266 · doi:10.1103/PhysRevD.86.065021

Abstract

It is known that the symmetric (massless) state of the Nambu--Jona-Lasinio model in 2+1 dimensions in a magnetic field B is not the ground state of the system at zero temperature due to the presence of a negative, linear in &|σ+iπ| $, t er min t h ee f f ec t i v e p o t e n t ia l f or t h eco m p os i t e f i e l d s$ σ\sim\barψψ $an d$ π\sim\barψiγ^5ψ $, w hi l e t h e q u a d r a t i c t er mi s a l w a y s p os i t i v e (a t a c h y o ni s ab se n t) . W e f in d t ha t f ini t e t e m p er a t u r e i s an ecess a r y in g r e d i e n t f or t h e t a c h y o ni c in s t abi l i t y o f t h esy mm e t r i cs t a t e t oocc u r . U t i l i z in g t h e S c h w in g er - - K e l d y s h r e a l - t im e f or ma l i s m w ec a l c u l a t e t h e d i s p er s i o n r e l a t i o n s f or t h e f l u c t u a t i o nm o d eso f t h eco m p os i t e f i e l d s$ σ $an d$ π$. We demonstrate the presence of the tachyonic instability of the symmetric state for coupling constant that exceeds a certain critical value which vanishes as temperature tends to zero in accordance with the phenomenon of magnetic catalysis.

13 pages, 2 figures

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Collective modes and Kosterlitz-Thouless transition in a magnetic field in the planar Nambu--Jona-Lasino model